MinT - Best Known (35−15, 35, s)-Nets in Base 4

Best Known (35−15, 35, s)-Nets in Base 4

(35−15, 35, 66)-Net over F₄ — Constructive and digital

Digital (20, 35, 66)-net over F₄, using

1 times m-reduction [i] based on digital (20, 36, 66)-net over F₄, using
- trace code for nets [i] based on digital (2, 18, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]

(35−15, 35, 941)-Net in Base 4 — Upper bound on s

There is no (20, 35, 942)-net in base 4, because

1 times m-reduction [i] would yield (20, 34, 942)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 297 097966 226380 242700 > 4³⁴ [i]